All things Riemannian: metrics, (sub)manifolds and gradients
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Description
This lecture covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, smooth curves, Riemannian metrics, smooth vector fields, and Euclidean spaces with inner products.
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We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemann
Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.
